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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

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If the probability density on a random vector is symmetric, then each variable is identically distributed?

Let $X$ be a random vector with joint distribution $F$ and density $f$. If $f$ is symmetric, is this equivalent to each random variable being identically distributed? We say $f$ is symmetric if it is invariant to a permutation in its arguments. For…
user91
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Showing that $p^n(1-p) \leq \frac{1}{en}$

I am reading a paper and found the following Lemma without a proof. Let $X_1, \ldots, X_{n+1}$ be independent Bernoulli random variables, where $\Pr[X_i = 1] = p$. Let $E$ be the event that the first $n$ variables are all $1$, but the $X_{n+1}$ is…
Sam Zadimoghaddam
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Expected number of cluster of cars

This question is based on a previously asked question, Probability problem: cars on the road. The question is: A road of infinite length has only one lane, so cars cannot overtake each other. $N$ cars are now put on the road. The cars travel at…
Ravi Upadhyay
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An elementary version of Laplace's Method of Succession

I'm currently taking a probability course, and in lecture, my professor went over an example which he called Laplace's method of succession. Basically, there are $n+1$ cards, $k$ of which are successes (the $k$ is uniformly distributed). A $k$ is…
John Lee
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Geometric distribution with multiple successes

Here's the question: "A sales representative vows to keep knocking on doors until he makes two sales. Given that his probability of success is $u$, let $X$ = the number of doors he knocks on. Find the probability mass function of $X$" My…
TrainChooseChoo
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Throw a dice 4 times. What is the probability `6` be up at-least one time?

First time I approach a probability question (: Throw a dice 4 times. What is the probability 6 be up at-least one time? Intuitively, I would say: $\frac{1}{6}\times4$. I would explain as: If you throw one time, probability is $\frac{1}{6}$. If…
Billie
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Binomial/Poisson distribution question

Someone asked me to help with assignment, but I am confused about the question, so basically, it is really easy: Batches of 100 components have a mean number of 5 defects per batch. What is the probability at least 9 defective component in a batch?…
Lost1
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Sam Harris' theory of probability on the Second Coming of Christ

Sam Harris (a famous atheist) argues in an interview with Cenk Uygur that the probability of Jesus Christ coming back to Jackson County, Missouri, USA is less likely than the probability of Jesus Christ coming back anywhere on Earth. He says that…
Steve McQueen
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Probability of choosing the correct stick out of a hundred. Challenge from reality show.

So I was watching the amazing race last night and they had a mission in which the contestants had to eat from a bin with 100 popsicles where only one of those popsicles had a writing on its stick containing the clue. Immediately I thought well of…
raam86
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Probability of familiarity with a popular item?

I want to know if there's a method for determining the likelihood that a person is familiar with the most popular item in a set, given the number of items in said set they are familiar with. Here's the best example I can think of: Andrew walks into…
Fibericon
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Almost equal probable sums with loaded dice

It's known that it's impossible to assign probabilities to a pair of loaded dice so that the sums $2,...,12$ are equally probable. How would one set the probabilities $\{p_i: 1\le i\le 6\}$ and $\{q_i: 1\le i\le 6\}$ for the two dice so that…
Katy
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Four consecutive heads from ten coin flips

If we flip a fair coin $10$ times, what is the probability we get $\ge 4$ consecutive heads? An approach would be to consider the probability of all consecutive heads, cut off by tails, e.g., HHHHTxxxxx THHHHTxxxx ... HHHHHTxxxx THHHHHTxxxx ... but…
boaten
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Probability of birthday in a group of N people

What is the probability that on any chosen given day (e.g. today) there is at least one person (in a group of N) who is celebrating his birthday? I would say the answer is either $N/365$ because you get $\frac{1}{365}+\frac{1}{365}$..$N$ times or…
gyosko
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Optimal strategy for picking cards: win a dollar for red, lose one for black, and stop at any time

Suppose I have four cards: two black, two red. I draw them one by one. Every time I draw a red card, I win a dollar, and every time I draw a black card, I lose a dollar. I can choose to stop at any time I want. What is the optimal strategy for…
user43123
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Coin pair betting paradox (NOT!)

If we throw two fair coins then there are 4 equally probable possibilities: HH, TT, HT, TH. Suppose we can't see the result, but we can check one of those two coins. (doesn't matter which one) Suppose the checked one is H. Then we know that both of…
cod3r
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